What it means
The words due and immediate describe when payments are made. In an annuity due, the first payment is made right away, on the day the contract begins, and later payments follow at the start of each period.
In an ordinary annuity, the first payment comes one period later, at the end of the first period. That small difference in timing has a real value.
Money received earlier can be spent or invested sooner, so each payment is worth more today. For this reason an annuity due costs more to buy than an ordinary annuity that pays the same amount.
Because the annuity runs for life, the insurer must weigh each payment by the chance that the person is still alive to receive it. The first payment is certain, because it is made on day one, while the later ones become less likely as time passes.
Present value is the sum of each payment multiplied by its survival probability and discounted for time. A typical use is retirement income where the person needs cash at the start of each month to pay rent and bills.
It also appears in pension valuations, where an actuary (a specialist in insurance and pension mathematics) must decide whether benefits are paid in advance or in arrears. Choosing the wrong convention can shift a valuation by a few per cent.
For non-specialists, the main lesson is to read the contract wording. If payments are made in advance, the annuity due formula applies, and the price will be higher than for payments in arrears.
Always confirm the payment dates before comparing quotes. Survival probabilities come from mortality tables, which are published statistics on how many people of each age are expected to survive.
Actuaries update these tables as life expectancy changes. Even a small improvement in longevity raises the cost of every life annuity, whether it pays in advance or in arrears.
In practice
Real-world examples.
Example
A retired teacher buys an annuity that pays her $2,000 on the first day of each month for life. She chose payments in advance because her rent is due on the first of the month. The monthly income is slightly smaller than an arrears contract would give, which she regards as a fair price for the convenience.
Example
An actuary values a company pension scheme where benefits are paid at the start of each quarter. She uses the annuity due convention and shows the board that the liability is higher than if payments were made in arrears.
Example
A financial adviser compares two annuity quotes for a client, and finds that one pays in advance while the other pays in arrears. After adjusting for timing, the quotes are much closer than the headline numbers suggested. He explains the difference to the client so that the final choice rests on the guarantees and the insurer's strength.
Formula
Calculation
Present value = sum over each payment of (payment x probability of being alive at that date) / (1 + interest rate) raised to the number of years
Suppose a whole life annuity due pays $10,000 at the start of each year. For a simplified illustration, assume the buyer is certain to be alive at the first payment, 98% likely at the second and 95% likely at the third, with a discount rate of 5% and only three payments considered. PV = 10,000 + (10,000 x 0.98) / 1.05 + (10,000 x 0.95) / 1.1025. The second term is 9,800 / 1.05 = $9,333.33 and the third term is 9,500 / 1.1025 = $8,616.78. PV = 10,000 + 9,333.33 + 8,616.78 = $27,950.11.Case study
Seen in the real world.
Brookside Pension Services is an illustrative, fictional firm that administers pension schemes. It valued the benefits of a scheme using payments at the end of each year, but the scheme rules actually paid pensions at the start of each year.
A reviewer noticed the mismatch. With a discount rate of 5%, the correction increased the present value of each payment by a factor of 1.05, so a liability of $20,000,000 became 20,000,000 x 1.05 = $21,000,000, an increase of $1,000,000.
The scheme's trustees increased the funding plan to match, and the administrator added a check of payment timing to its procedures. The illustrative lesson is that a small timing assumption can create a large difference in the value of long-dated obligations. Brookside also asked an independent actuary to review the other schemes it administered for the same error, and found one further case.
Watch out
Common mistakes.
- Using the ordinary annuity formula for payments made in advance, which understates the value.
- Forgetting that a life annuity is also weighted by the chance of survival, when treating it as a fixed-term annuity.
- Comparing annuity quotes without checking whether payments are made at the start or the end of each period.
Questions
People also ask.
How do I convert between ordinary annuity and annuity due?
Multiply the present value of an ordinary annuity by one plus the interest rate for the period to get the annuity due value.
Why does an annuity due cost more?
Each payment arrives one period earlier, so it is worth more in today's money.
Is the first payment always certain?
In an annuity due the first payment is made at the outset, so it is usually treated as certain, while later payments depend on survival.
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